# Turbo Machines - Mechanical Engineering (MCQ) questions and answers for Q. 10895

Q.  What is the formula for forces exerted by fluid on a body?
- Published on 16 Sep 15

a. (Rate of momentum in) x (Rate of momentum out)
b. (Rate of momentum in) – (Rate of momentum out)
c. (Rate of momentum in) + (Rate of momentum out)
d. None of the above

ANSWER: (Rate of momentum in) – (Rate of momentum out)

#### Discussion

• Pankaj   -Posted on 06 Oct 15
We know that the product of mass and velocity is called as momentum.

∴ Momentum = m x V

Magnitude of applied force is rate of change of momentum

∴ Applied force F = d/dt (m x V)

On differentiating the above equation,

F = (m x (dV/dt)) + (V x (dm/dt))

In solid bodies mass of body remains constant,

∴ dm/dt = 0

F = (m x (dV/dt))

∴ F = m x dV/dt

= (m/t) (V2 – V1 )

Mass flow rate of fluid, ṁ = (m/t) = ρ x Q

Therefore force exerted by the body on fluid is given by,

F = ρ Q (V2 – V1 )

Thus the force exerted by fluid on body will be equal and opposite to the force exerted by the body on fluid.

F = ρ Q (V1 – V2 )

Therefore,

Force exerted by fluid on body = Rate of momentum in (ṁ V1) – Rate of momentum out (ṁ V2)

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